A Flow-Driven Cavity as an Air Cycling Model for Window Flow
Abstract
Keywords: computational fluid dynamics, CFD, incompressible, Paraview, R, Python, coe347, spring 2022, window, building, tornado, high, reynolds, unsteady, steady, stress, strain, rate, mixing, volumetric, flow.
Motivation
For severe storms, it is widely known that puncture damage is the primary cause of failure for most buildings and aircraft. Once a puncture has been created, the resultant pressure differential can cause fast inflow and damage to the interior. We seek to study this inflow, and stresses near the opening walls, which can cause structural issues leading to collapse of one or more walls.
Most relevant studies use incredibly large amounts of computational power, due to the large scale of the problem (Reynolds numbers for tornadoes and hurricanes can easily start in the millions). We seek to show the applicability of lower Reynolds simulations to higher Reynolds situations, since the general large-scale flow structure remains the same.
# Implementation {.chapter}
We implement all simulation with OpenFoam, analysis with Paraview and Python3, and documentation code in R Xie, Dervieux, and Riederer (2020).
Mesh Assembly
We assemble a 2D mesh template as below, with the following parameters, all lengths nondimensionalized in terms of dimension \(L\):
mutable: wall thickness \(w\), window width \(a\),
immutable: window location \(b=0.5\), cavity height \(H=1\), cavity width \(L=1\), and free-stream width \(2e=0.1\).
Two sets of simulations are performed, one for the low Reynolds (\(Re\)) numbers of 10 and 200, which will be shown to be steady, and another for \(Re=1000, 10000\).
Each mesh also has a corresponding refinement, which is described by the \(meshFactor\) parameter, representing the refinement in each dimension.
Full lists are available below.
Meshes for the Low Reynolds simulations
| meshfactor | Reynolds | window.a. | wall.w. |
|---|---|---|---|
| 5 | 10 | 0.05 | 0.05 |
| 5 | 10 | 0.05 | 0.10 |
| 5 | 10 | 0.50 | 0.05 |
| 5 | 10 | 0.50 | 0.10 |
| 10 | 10 | 0.05 | 0.05 |
| 10 | 10 | 0.05 | 0.10 |
| 10 | 10 | 0.50 | 0.05 |
| 10 | 10 | 0.50 | 0.10 |
| 5 | 200 | 0.05 | 0.05 |
| 5 | 200 | 0.05 | 0.10 |
| 5 | 200 | 0.50 | 0.05 |
| 5 | 200 | 0.50 | 0.10 |
| 10 | 200 | 0.05 | 0.05 |
| 10 | 200 | 0.05 | 0.10 |
| 10 | 200 | 0.50 | 0.05 |
| 10 | 200 | 0.50 | 0.10 |
Meshes for the High Reynolds simulations
| meshfactor | Reynolds | window.a. | wall.w. |
|---|---|---|---|
| 3 | 1000 | 0.5 | 0.1 |
| 5 | 1000 | 0.5 | 0.1 |
| 3 | 10000 | 0.5 | 0.1 |
| 5 | 10000 | 0.5 | 0.1 |
BlockMeshDict and similar files are available at the repository.
Mesh Images
A couple mesh samples are shown here; see the appendix for all images.
meshFactor, Re, windowWidth, wallThickness=5, 10, 0.05, 0.05:
meshFactor, Re, windowWidth, wallThickness=10, 200, 0.5, 0.1:
Now that the mesh resolutions can be seen as adequate, we will move to results.
Literature Review
- blank at the moment; will put some notes from the articles I sent out and hopefully some comparisions to cavity flow (to be referred to again later).
# Low Reynolds Number
General Solution Form
- show basic solution images here
Vortice Positions
- table of vortice positions
Window Wall Solution Profiles
- profiles for Left and Right
Cavity Midline Solution Profile
- midline profiles
# High Reynolds Number - Part 1
General Solution Form
- show basic solution images here for both Re and make general arguments
Strouhal Number and Vortex Shedding
- FFT plots
- STFT plots
- table of values for Strouhal
Volumetric Flow Rate and Mixing
- plots
- generic argument / example for UAV and
Window Wall Strain Rate
T = 1.47 (unsteady startup)
T = 60 (steady-state for large-scales of flow)
Maximum Strain Rate over Time
High Reynolds Number - Part 2
Conclusions
References
Appendix
Mesh Images
Mesh Images for the Low Reynolds simulations (same order)
Mesh Images for the High Reynolds simulations (same order)
Acknowledgements
Thank you so much for reading this work!